Related papers: A Note on the Sonar Transform and Related Radon Tr…
The Funk-Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk-Radon transform has been generalized to…
We present a novel analysis of a Radon transform, $R$, which maps an $L^2$ function of compact support to its integrals over smooth surfaces of revolution with centers on an embedded hypersurface in $\mathbb{R}^n$. Using microlocal…
The Hua-Radon and polarized Hua-Radon transform are two orthogonal projections defined on holomorphic functions in the Lie sphere. Both transformations can be written as integral transforms with respect to a suitable reproducing kernel.…
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…
This paper deals with various topics in analysis on hyperbolic spaces. It surveys some recent progress in non-Euclidean Fourier Analysis and proves some new results for the geodesic Radon transform on hyperbolic spaces.
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
The paper studies various properties of the V-line transform (VLT) in the plane and conical Radon transform (CRT) in $\mathbb{R}^n$. VLT maps a function to a family of its integrals along trajectories made of two rays emanating from a…
We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$.
Harmonic maps from $\BR^2$ or one-connected domain ${\O}\subset \BR^2$ into $GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the B\"acklund-Darboux transformation is applied to the case of the harmonic maps. A new general formula on…
Convolution with an appropriate surface measure on a paraboloid in R^d defines a bounded operator T from L^p(R^d) to L^q(R^d) for certain exponents p,q. In this article it is proved that there exist functions which extremize the associated…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
The spherical means Radon transform $\mathcal{M}f(x,r)$ is defined by the integral of a function $f$ in $\mathbb{R}^{n}$ over the sphere $S(x,r)$ of radius $r$ centered at a $x$, normalized by the area of the sphere. The problem of…
One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on…
In this paper we investigate the mapping properties in Lebesgue-type spaces of certain generalized Radon transforms defined by integration over curves.
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of the Funk-Radon transform, which is a flexible alternative to…
The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit…
In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transform, which assigns to a function its integrals along full…
We present an analysis of a novel spherical Radon transform, $R$, which defines the integrals of a function, $f$, in $\mathbb{R}^n$ over spheres with arbitrary center ($\mathbf{y}$) and radii, $r(\mathbf{y})$, which vary smoothly with…